Yeah, he gets it right... because, look, if you try to add both the digits of a two digit number, and subract it with the original, it always gives a multiple of nine. And if look in the paper that the gopher gives us, it has the same symbol for the multiples of nine. He changes the card each time because we'll get a doubt if the same symbol comes again and again.
For example:
65= 6+5=11
65-11=54
54=6*9
Another one:
79=7+9=16
79-16=63
63=7*9
And even though it's the same multiple, you'll get different symbols...
PS: Please don't take this in the wrong way. I don't want to criticise the game. It's just that I've figured out the logic:)

Of course he gets it right. You subtract the two nubers added from the original number. Example: 43. You subtract 4+3. Instead of taking 43-7, take 43 -3 -4. You will get the same answer. However this proves that no matter what nuber you choose you will always subtract the second number (in this case 3) to get a number that ends with 0 (in this case 40). Then the nuber you subtracted second can only be 1, 2, 3, 4, 5, 6, 7, 8 or 9 And the only possible outcomes will be, 90 - 9 = 81, 80 - 8 = 72, 70 - 7 = 63, 60 - 6 = 54, 50 - 5 = 45, 40 - 4= 36, 30 -3 = 27, 20 - 2 = 18 and 10 - 1 = 9. You might notice that all of these numbers are in the 9's multiplication table. That is because when multiplying by 9 you can instead multiply by 10 and subract the other number. For example: 5*9 = 5*10 - 5 = 50 - 5 = 45. First you add one 5 and then you subtract it again. 9*5 = 9*5 + 5 - 5.And all the symbol 90,81,72,63,54,45,36,27,18 and 9 are the same .